Hence, the circulation of the osmotic field does change with time and the Kelvin circulation theorem [1]}, [2]} is violated. It is important to note that as with the entropy production and the tensor equation (27), the non-zero vorticity effect is again a general result following from the inclusion of an imaginary quantum potential and does not rely on the phase assumption mentioned in section 2. It can be immediately verified that the same result holds by substituting the exact expression (10) in (30).
